Find a vector equation and parametric equations for the line segment that joins P to Q. P(0,0,0) Q(−5,6,6)

Answers

Answer 1

Answer:

Answer:

The vector that goes from point P to point Q is:

PQ = (-5, 6, 6) - (0, 0, 0) = (-5, 6, 6)

To find the vector equation for the line segment that joins P to Q, we need to add a parameter t that varies from 0 to 1 to the vector equation of the line going from P to Q:

r(t) = P + t(PQ) = (0, 0, 0) + t(-5, 6, 6) = (-5t, 6t, 6t)

To find the parametric equations for the line segment, we can isolate each coordinate:

x = -5t

y = 6t

z = 6t

Solving for t in each equation, we get:

t = -x/5

t = y/6

t = z/6

We can see that the parameter t varies from 0 to 1 as x goes from 0 to -5, as y goes from 0 to 6, and as z goes from 0 to 6. Therefore, the parametric equations for the line segment that joins P to Q are:

x = -5t

y = 6t

z = 6t

where 0 ≤ t ≤ 1.

Step-by-step explanation:

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Of the 15 students in Danielle's class, 5 went to the zoo and the rest went to the aquarium. What is the ratio of the number of students who went to the aquarium to the total number of students?

Answers

Answer:

15:20=3:4

Step-by-step explanation:

Simplify the expression below.
√169

Answers

Answer:

The simplified form of the given expression is 13.

Step-by-step explanation:

The given expression is

$√(169)$

It can be written as

$√(13* 13)$

$√(13^2)$

$(13^2)^{(1)/(2)}$ $[\because √(x)=x^{(1)/(2)}]$

$13^{(2)/(2)}$ $[\because (x^m)^n=x^(mn)]$

$13^(1)$

$13$

Therefore the simplified form of the given expression is 13.

The square root of 169 is 13 because 13X13 equals to 169.

Rewrite in simplest radical form x^ 5/6 over x^ 1/6 show each step of your process

Answers

Answer:

The simplest Radical = $\sqrt{x^(3) }$

Step-by-step explanation:

The two terms of the fraction are $x^{(5)/(6)}$ ⇒numerator

and $x^{(1)/(6)}$ ⇒denominator

Both of them are same variable x

So we can use the rule of the power:

If we divide to terms have the same base we subtract their powers

$\frac{x^{(5)/(6) } }{x^{(1)/(6) } }=x^{(5)/(6)-(1)/(6) }=x^{(4)/(6) } =x^{(2)/(3) }$

If the power is in the shape of fraction so the numerator of the fraction represents the radical and the denominator represents the power inside the radical.

$x^{(2)/(3) }=\sqrt{x^(3) }$

Answer: $\bold{\sqrt[3]{x^2} }$

Step-by-step explanation:

$\frac{x^{(5)/(6)}}{x^{(1)/(6)}}\n\n\n=x^{(5)/(6)-(1)/(6)}}}\n\n\n=x^{(4)/(6)}}}\n\n\n=x^{(2)/(3)}}}\n\n=\sqrt[3]{x^2}$

Two joggers, one averaging 7 mph and one averaging 5 mph, start from a designated initial point. The slower jogger arrives at the end of the run 45 minutes after the other jogger. Find fhe distance of the run.

Answers

22.5 miles long

basically all you have to do is count out the factors until you reach two number of 45 apart

  DIFFERENCE
7MPH 5MPH BETWEEN THEM

7 5 2
14 10 4
21 15   6
28 20 8
35 25 10
42 30 12
49 35 14
56 40 16
63 45 18
70 50   20
77 55   22
84 60   24
91 65 26
98    70 28
105    75 30
112    80 32
119 85 34
126 90 36
133 95 38
140    100 40
147 105 42
154 110 44
161 115 46

considering the differences are even it means it has to fall in the middle. if you count from the top it is 22.5 numbers down giving you the number of miles.
I'm sure there is an easier way but this is how i would solve it. :)

Final answer:

The distance of the run is 13.125 miles. The total time for the slower jogger was found to be 2.625 hours. Thus, both joggers ran the same distance, but at different speeds resulting in different finish times.

Explanation:

The problem deals with the concept of relative speed in mathematics. To find the distance of the run, we first need to figure out the time it took for each jogger to finish the run. We know that the slower jogger finished 45 minutes after the faster one. Since the speed equivalence is expressed in miles per hour (mph), let's convert 45 minutes into hours by dividing 45 by 60, giving us 0.75 hours.

Given that the slower jogger runs at 5 mph, and they took 0.75 hours longer than the faster one, we know they ran for a certain time 't', so we can represent this as t = total time of slower jogger's run.

The faster jogger ran at 7 mph. Since the jogger was 0.75 hours ahead of the slower one, the time would be represented by t - 0.75 hours = total time of faster jogger's run. The distance travelled by each jogger is 'speed x time'.

Following this, we equal these distances because it's the same course: 5t = 7(t - 0.75).

Solving this equation gives us t = 2.625 hours (total time for slower jogger). To find the run's distance, we can now substitute total time into either jogger's speed x time calculation. We'll use the slower jogger here: Distance = 5t = 5*2.625 = 13.125 miles.

Learn more about Relative Speed here:

brainly.com/question/14362959

#SPJ3

which of these correctly rearranges the terms in this polynomial so like terms are next to each other ? 3-6x+4x^2+3x-6x^2-4 PLEASE HELP!!

Answers

Answer:

A is the answer

Step-by-step explanation:

Answer:

the answer is A.

Step-by-step explanation:

kelly is training for one marathon in week one she runs 7 miles in week two she runs 10 miles in week 3 she runs 13 miles given that she keeps the same pattern find the total distance kelly has run after practicing for 7 weeks

Answers

Answer:

25 miles on week 7

Step-by-step explanation:

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